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2011-02-24 | Environment-assisted quantum Minority games | The effect of entanglement and correlated noise in a four-player quantum
Minority game is investigated. Different time correlated quantum memory
channels are considered to analyze the Nash equilibrium payoff of the 1st
player. It is seen that the Nash equilibrium payoff is substantially enhanced
due to the presence of correlated noise. The behaviour of damping channels
(amplitude damping and phase damping) is approximately similar. However,
bit-phase flip channel heavily influences the minority game as compared to
other channels in the presence of correlated noise. On the other hand, phase
flip channel has a symmetrical behaviour around 50% noise threshold. The
significant reduction in payoffs due to decoherence is well compensated due to
the presence of correlated noise. However, the Nash equilibrium of the game
does not change in the presence of noise. It is seen that in case of
generalized amplitude damping channel, entanglement plays a significant role at
lower level of decoherence. The channel has less dominant effects on the payoff
at higher values of decoherence. Furthermore, amplitude damping and generalized
amplitude damping channels have almost comparable effects at lower level of
decoherence $(p<0.5)$. Therefore, the game deserves careful study during its
implementation due to prominent role of noise for different channels. | 1102.5056v2 |
2011-03-17 | Viscous damping of r-modes: Large amplitude saturation | We analyze the viscous damping of r-mode oscillations of compact stars,
taking into account non-linear viscous effects in the large-amplitude regime.
The qualitatively different cases of hadronic stars, strange quark stars, and
hybrid stars are studied. We calculate the viscous damping times of r-modes,
obtaining numerical results and also general approximate analytic expressions
that explicitly exhibit the dependence on the parameters that are relevant for
a future spindown evolution calculation. The strongly enhanced damping of large
amplitude oscillations leads to damping times that are considerably lower than
those obtained when the amplitude dependence of the viscosity is neglected.
Consequently, large-amplitude viscous damping competes with the gravitational
instability at all physical frequencies and could stop the r-mode growth in
case this is not done before by non-linear hydrodynamic mechanisms. | 1103.3521v2 |
2011-05-01 | Viscous damping of nanobeam resonators: humidity, thermal noise and the paddling effect | The nanobeam resonator is the key mechanical component in the
nano-electromechanical system. In addition to its high frequency originating
from its low dimension, the performance is significantly influenced by the
circumstances, especially at nanoscale where a large surface area of the
material is exposed. Molecular dynamics simulations and theoretical analysis
are used for a quantitative prediction on the damping behavior, such as the
critical damping condition and lifetime, of nanobeam resonators that directly
maps the fluid-structure properties and interaction information into dynamical
behaviors. We show here how the humidity defines the critical damping condition
through viscous forces, marking the transition from under-damping to
over-damping regime at elevated humidity. Novel phenomena such as the thermal
fluctuation and paddling effects are also discussed. | 1105.0139v1 |
2011-06-07 | Damping by branching: a bioinspiration from trees | Man-made slender structures are known to be sensitive to high levels of
vibration, due to their flexibility, which often cause irreversible damage. In
nature, trees repeatedly endure large amplitudes of motion, mostly caused by
strong climatic events, yet with minor or no damage in most cases. A new
damping mechanism inspired by the architecture of trees is here identified and
characterized in the simplest tree-like structure, a Y-shape branched
structure. Through analytical and numerical analyses of a simple
two-degree-of-freedom model, branching is shown to be the key ingredient in
this protective mechanism that we call damping-by-branching. It originates in
the geometrical nonlinearities so that it is specifically efficient to damp out
large amplitudes of motion. A more realistic model, using flexible beam
approximation, shows that the mechanism is robust. Finally, two bioinspired
architectures are analyzed, showing significant levels of damping achieved via
branching with typically 30% of the energy being dissipated in one oscillation.
This concept of damping-by-branching is of simple practical use in the design
of slender flexible structures. | 1106.1283v1 |
2011-11-29 | Dispersion and damping of potential surface waves in a degenerate plasma | Potential (electrostatic) surface waves in plasma half-space with degenerate
electrons are studied using the quasi-classical mean-field kinetic model. The
wave spectrum and the collisionless damping rate are obtained numerically for a
wide range of wavelengths. In the limit of long wavelengths, the wave frequency
$\omega$ approaches the cold-plasma limit $\omega=\omega_p/\sqrt{2}$ with
$\omega_p$ being the plasma frequency, while at short wavelengths, the wave
spectrum asymptotically approaches the spectrum of zero-sound mode propagating
along the boundary. It is shown that the surface waves in this system remain
weakly damped at all wavelengths (in contrast to strongly damped surface waves
in Maxwellian electron plasmas), and the damping rate nonmonotonically depends
on the wavelength, with the maximum (yet small) damping occuring for surface
waves with wavelength of $\approx5\pi\lambda_{F}$, where $\lambda_{F}$ is the
Thomas-Fermi length. | 1111.6723v1 |
2012-01-29 | Smooth attractors of finite dimension for von Karman evolutions with nonlinear frictional damping localized in a boundary layer | In this paper dynamic von Karman equations with localized interior damping
supported in a boundary collar are considered. Hadamard well-posedness for von
Karman plates with various types of nonlinear damping are well-known, and the
long-time behavior of nonlinear plates has been a topic of recent interest.
Since the von Karman plate system is of "hyperbolic type" with critical
nonlinearity (noncompact with respect to the phase space), this latter topic is
particularly challenging in the case of geometrically constrained and nonlinear
damping. In this paper we first show the existence of a compact global
attractor for finite-energy solutions, and we then prove that the attractor is
both smooth and finite dimensional. Thus, the hyperbolic-like flow is
stabilized asymptotically to a smooth and finite dimensional set.
Key terms: dynamical systems, long-time behavior, global attractors,
nonlinear plates, nonlinear damping, localized damping | 1201.6072v1 |
2012-06-15 | Landau Damping in a Turbulent Setting | To address the problem of Landau damping in kinetic turbulence, the forcing
of the linearized Vlasov equation by a stationary random source is considered.
It is found that the time-asymptotic density response is dominated by resonant
particle interactions that are synchronized with the source. The energy
consumption of this response is calculated, implying an effective damping rate,
which is the main result of this paper. Evaluating several cases, it is found
that the effective damping rate can differ from the Landau damping rate in
magnitude and also, remarkably, in sign. A limit is demonstrated in which the
density and current become phase-locked, which causes the effective damping to
be negligible; this potentially resolves an energy paradox that arises in the
application of critical balance to a kinetic turbulence cascade. | 1206.3415v4 |
2013-10-29 | Influence of sample geometry on inductive damping measurement methods | We study the precession frequency and effective damping of patterned
permalloy thin films of different geometry using integrated inductive test
structures. The test structures consist of coplanar wave guides fabricated onto
patterned permalloy stripes of different geometry. The width, length and
position of the permalloy stripe with respect to the center conductor of the
wave guide are varied. The precession frequency and effective damping of the
different devices is derived by inductive measurements in time and frequency
domain in in-plane magnetic fields. While the precession frequencies do not
reveal a significant dependence on the sample geometry we find a decrease of
the measured damping with increasing width of the permalloy centered underneath
the center conductor of the coplanar wave guide. We attribute this effect to an
additional damping contribution due to inhomogeneous line broadening at the
edges of the permalloy stripes which does not contribute to the inductive
signal provided the permalloy stripe is wider than the center conductor.
Consequences for inductive determination of the effective damping using such
integrated reference samples are discussed. | 1310.7817v1 |
2014-04-02 | Determination of the cross-field density structuring in coronal waveguides using the damping of transverse waves | Time and spatial damping of transverse magnetohydrodynamic (MHD) kink
oscillations is a source of information on the cross-field variation of the
plasma density in coronal waveguides. We show that a probabilistic approach to
the problem of determining the density structuring from the observed damping of
transverse oscillations enables us to obtain information on the two parameters
that characterise the cross-field density profile. The inference is performed
by computing the marginal posterior distributions for density contrast and
transverse inhomo- geneity length-scale using Bayesian analysis and damping
ratios for transverse oscillations under the assumption that damping is
produced by resonant absorption. The obtained distributions show that, for
damping times of a few oscillatory periods, low density contrasts and short
inho- mogeneity length scales are more plausible in explaining observations.
This means that valuable information on the cross-field density profile can be
obtained even if the inversion problem, with two unknowns and one observable,
is a mathematically ill-posed problem. | 1404.0584v1 |
2014-04-14 | Distributed Approximate Message Passing for Compressed Sensing | In this paper, an efficient distributed approach for implementing the
approximate message passing (AMP) algorithm, named distributed AMP (DAMP), is
developed for compressed sensing (CS) recovery in sensor networks with the
sparsity K unknown. In the proposed DAMP, distributed sensors do not have to
use or know the entire global sensing matrix, and the burden of computation and
storage for each sensor is reduced. To reduce communications among the sensors,
a new data query algorithm, called global computation for AMP (GCAMP), is
proposed. The proposed GCAMP based DAMP approach has exactly the same recovery
solution as the centralized AMP algorithm, which is proved theoretically in the
paper. The performance of the DAMP approach is evaluated in terms of the
communication cost saved by using GCAMP. For comparison purpose, thresholding
algorithm (TA), a well known distributed Top-K algorithm, is modified so that
it also leads to the same recovery solution as the centralized AMP. Numerical
results demonstrate that the GCAMP based DAMP outperforms the Modified TA based
DAMP, and reduces the communication cost significantly. | 1404.3766v2 |
2014-12-17 | The most metal-rich damped Lyman alpha systems at z>1.5 I: The Data | We present HIRES observations for 30 damped Lyman alpha systems, selected on
the basis of their large metal column densities from previous, lower resolution
data. The measured metal column densities for Fe, Zn, S, Si, Cr, Mn, and Ni are
provided for these 30 systems. Combined with previously observed large metal
column density damped Lyman alpha systems, we present a sample of 44 damped
Lyman alpha systems observed with high resolution spectrographs (R~30000).
These damped Lyman alpha systems probe the most chemically evolved systems at
redshifts greater than 1.5. We discuss the context of our sample with the
general damped Lyman alpha population, demonstrating that we are probing the
top 10% of metal column densities with our sample. In a companion paper, we
will present an analysis of the sample's elemental abundances in the context of
galactic chemical enrichment. | 1412.5491v1 |
2015-03-26 | Transient nutations decay in diluted paramagnetic solids: a radiation damping mechanism | Here, a theory of the intensity and concentration dependent damping of
nutation signals observed by Boscaino et al. (Phys. Rev B 48, 7077 (1993);
Phys. Rev. A 59, 4087 (1999)) and by others in various two-level spin systems
is proposed. It is shown that in diluted paramagnetic solids contribution of
dipole-dipole interaction to the nutation decay is negligibly small. We
elaborated a cavity loss (radiation damping) mechanism that explains the
intensity- and concentration dependence of the damping. It is shown that
instead of ordinary Bloch's transverse T2 and longitudinal T1 damping
parameters the decay of transverse and longitudinal spin components in nutation
process are described by one and the same intensity-, concentration-,
frequency- and time dependent damping parameter. | 1503.07641v2 |
2015-08-17 | Increased magnetic damping of a single domain wall and adjacent magnetic domains detected by spin torque diode in a nanostripe | We use spin-torque resonance to probe simultaneously and separately the
dynamics of a magnetic domain wall and of magnetic domains in a nanostripe
magnetic tunnel junction. Thanks to the large associated resistance variations
we are able to analyze quantitatively the resonant properties of these single
nanoscale magnetic objects. In particular, we find that the magnetic damping of
both domains and domain walls is doubled compared to the damping value of their
host magnetic layer. We estimate the contributions to damping arising from
dipolar couplings between the different layers in the junction and from the
intralayer spin pumping effect. We find that they cannot explain the large
damping enhancement that we observe. We conclude that the measured increased
damping is intrinsic to large amplitudes excitations of spatially localized
modes or solitons such as vibrating or propagating domain walls | 1508.04043v1 |
2016-04-27 | Influence of nonlocal damping on the field-driven domain wall motion | We derive the complete expression of nonlocal damping in noncollinear
magnetization due to the nonuniform spin current pumped by precessional
magnetization and incorporate it into a generalized Thiele equation to study
its effects on the dynamics of the transverse and vortex domain walls (DWs) in
ferromagnetic nanowires. We demonstrate that the transverse component of
nonlocal damping slows down the field-driven DW propagation and increases the
Walker breakdown field whereas it is neglected in many previous works in
literature. The experimentally measured DW mobility variation with the damping
tuned by doping with heavy rare-earth elements that had discrepancy from
micromagnetic simulation are now well understood with the nonlocal damping. Our
results suggest that the nonlocal damping should be properly included as a
prerequisite for quantitative studies of current-induced torques in
noncollinear magnetization. | 1604.07971v2 |
2016-04-27 | Damping of the Collective Amplitude Mode in Superconductors with Strong Electron-Phonon Coupling | We study the effect of strong electron-phonon interactions on the damping of
the Higgs amplitude mode in superconductors by means of non-equilibrium
dynamical mean-field simulations of the Holstein model. In contrast to the BCS
dynamics, we find that the damping of the Higgs mode strongly depends on the
temperature, becoming faster as the systen approaches the transition
temperature. The damping at low temperatures is well described by a power-law,
while near the transition temperature the damping shows exponential-like
behavior. We explain this crossover by a temperature-dependent quasiparticle
lifetime caused by the strong electron- phonon coupling, which smears the
superconducting gap edge and makes the relaxation of the Higgs mode into
quasiparticles more efficient at elevated temperatures. We also reveal that the
phonon dynamics can soften the Higgs mode, which results in a slower damping. | 1604.08073v2 |
2016-12-16 | Dynamics of cohering and decohering power under Markovian channels | In this paper, we investigate the cohering and decohering power for the
one-qubit Markovian channels with respect to coherence in terms of the
$l_{1}$-norm, the R$\acute{e}$nyi $\alpha$-relative entropy and the Tsallis
$\alpha$-relative entropy. In the case of $\alpha=2$, the cohering and
decohering power of the amplitude damping channel, the phase damping channel,
the depolarizing channel, and the flip channels under the three measures of
coherence are calculated analytically. The decohering power on the $x, y, z$
basis referring to the amplitude damping channel, the phase damping channel,
the flip channel for every measure we investigated is equal. This property also
happens in the cohering power of the phase damping channel, the depolarizing
channel, and the flip channels. However, the decohering power of the
depolarizing channel is independent to the reference basis, and the cohering
power of the amplitude damping channel on the $x, y$ basis is different to that
on the $z$ basis. | 1612.05355v1 |
2017-01-19 | Decoherence effects on multiplayer cooperative quantum games | We study the behavior of cooperative multiplayer quantum games [35,36] in the
presence of decoherence using different quantum channels such as amplitude
damping, depolarizing and phase damping. It is seen that the outcomes of the
games for the two damping channels with maximum values of decoherence reduce to
same value. However, in comparison to phase damping channel, the payoffs of
cooperators are strongly damped under the influence\ amplitude damping channel
for\ the lower values of decoherence parameter. In the case of depolarizing
channel, the game is a no-payoff game irrespective of the degree of
entanglement in the initial state for the larger values of decoherence
parameter. The decoherence gets the cooperators worse off. | 1701.05342v1 |
2017-07-30 | Blow-up for semilinear damped wave equations with sub-Strauss exponent in the scattering case | It is well-known that the critical exponent for semilinear damped wave
equations is Fujita exponent when the damping is effective. Lai, Takamura and
Wakasa in 2017 have obtained a blow-up result not only for super-Fujita
exponent but also for the one closely related to Strauss exponent when the
damping is scaling invariant and its constant is relatively small,which has
been recently extended by Ikeda and Sobajima. Introducing a multiplier for the
time-derivative of the spatial integral of unknown functions, we succeed in
employing the technics on the analysis for semilinear wave equations and
proving a blow-up result for semilinear damped wave equations with sub-Strauss
exponent when the damping is in the scattering range. | 1707.09583v3 |
2017-10-09 | Resonant absorption of surface sausage and surface kink modes under photospheric conditions | We study the effect of resonant absorption of surface sausage and surface
kink modes under photospheric conditions where the slow surface sausage modes
undergo resonant damping in the slow continuum and the surface kink modes in
the slow and Alfv\'{e}n continua at the transitional layers. We use recently
derived analytical formulas to obtain the damping rate (time). By considering
linear density and linear pressure profiles for the transitional layers, we
show that resonant absorption in the slow continuum could be an efficient
mechanism for the wave damping of the slow surface sausage and slow surface
kink modes whilst the damping rate of the slow surface kink mode in the
Alfv\'{e}n continuum is weak. It is also found that the resonant damping of the
fast surface kink mode is much stronger than that of the slow surface kink
mode, showing a similar efficiency as under coronal conditions. It is worth to
notice that the slow body sausage and kink modes can also resonantly damp in
the slow continuum for those linear profiles. | 1710.03350v2 |
2017-11-21 | Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey conjecture | This work is devoted to the nonexistence of global-in-time energy solutions
of nonlinear wave equation of derivative type with weak time-dependent damping
in the scattering and scale invariant range. By introducing some multipliers to
absorb the damping term, we succeed in establishing the same upper bound of the
lifespan for the scattering damping as the non-damped case, which is a part of
so-called Glassey conjecture on nonlinear wave equations. We also study an
upper bound of the lifespan for the scale invariant damping with the same
method. | 1711.07591v2 |
2018-01-03 | Stabilisation of wave equations on the torus with rough dampings | For the damped wave equation on a compact manifold with {\em continuous}
dampings, the geometric control condition is necessary and sufficient for
{uniform} stabilisation. In this article, on the two dimensional torus, in the
special case where $a(x) = \sum\_{j=1}^N a\_j 1\_{x\in R\_j}$ ($R\_j$ are
polygons), we give a very simple necessary and sufficient geometric condition
for uniform stabilisation. We also propose a natural generalization of the
geometric control condition which makes sense for $L^\infty$ dampings. We show
that this condition is always necessary for uniform stabilisation (for any
compact (smooth) manifold and any $L^\infty$ damping), and we prove that it is
sufficient in our particular case on $\mathbb{T}^2$ (and for our particular
dampings). | 1801.00983v2 |
2018-03-12 | Optical Rotation of Levitated Spheres in High Vacuum | A circularly polarized laser beam is used to levitate and control the
rotation of microspheres in high vacuum. At low pressure, rotation frequencies
as high as 6 MHz are observed for birefringent vaterite spheres, limited by
centrifugal stresses. Due to the extremely low damping in high vacuum,
controlled optical rotation of amorphous SiO$_2$ spheres is also observed at
rates above several MHz. At $10^{-7}$ mbar, a damping time of $6\times10^4$ s
is measured for a $10\ \mu$m diameter SiO$_2$ sphere. No additional damping
mechanisms are observed above gas damping, indicating that even longer damping
times may be possible with operation at lower pressure. The controlled optical
rotation of microspheres at MHz frequencies with low damping, including for
materials that are not intrinsically birefringent, provides a new tool for
performing precision measurements using optically levitated systems. | 1803.04297v1 |
2018-03-23 | A conservation law with spatially localized sublinear damping | We consider a general conservation law on the circle, in the presence of a
sublinear damping. If the damping acts on the whole circle, then the solution
becomes identically zero in finite time, following the same mechanism as the
corresponding ordinary differential equation. When the damping acts only
locally in space, we show a dichotomy: if the flux function is not zero at the
origin, then the transport mechanism causes the extinction of the solution in
finite time, as in the first case. On the other hand, if zero is a
non-degenerate critical point of the flux function, then the solution becomes
extinct in finite time only inside the damping zone, decays algebraically
uniformly in space, and we exhibit a boundary layer, shrinking with time,
around the damping zone. Numerical illustrations show how similar phenomena may
be expected for other equations. | 1803.08767v1 |
2019-03-06 | Microwave magnon damping in YIG films at millikelvin temperatures | Magnon systems used in quantum devices require low damping if coherence is to
be maintained. The ferrimagnetic electrical insulator yttrium iron garnet (YIG)
has low magnon damping at room temperature and is a strong candidate to host
microwave magnon excitations in future quantum devices. Monocrystalline YIG
films are typically grown on gadolinium gallium garnet (GGG) substrates. In
this work, comparative experiments made on YIG waveguides with and without GGG
substrates indicate that the material plays a significant role in increasing
the damping at low temperatures. Measurements reveal that damping due to
temperature-peak processes is dominant above 1 K. Damping behaviour that we
show can be attributed to coupling to two-level fluctuators (TLFs) is observed
below 1 K. Upon saturating the TLFs in the substrate-free YIG at 20 mK,
linewidths of 1.4 MHz are achievable: lower than those measured at room
temperature. | 1903.02527v3 |
2020-05-15 | Slow magnetosonic wave absorption by pressure induced ionization-recombination dissipation | A new mechanisms for damping of slow magnetosonic waves (SMW) by pressure
induced oscillations of the ionization degree is proposed. An explicit formula
for the damping rate is quantitatively derived. Physical conditions where the
new mechanism will dominate are briefly discussed. The ionization-recombination
damping is frequency independent and has no hydrodynamic interpretation.
Roughly speaking large area of partially ionized plasma are damper for basses
of SMW while usual MHD mechanisms operate as a low pass filter. The derived
damping rate is proportional to the square of the sine between the constant
magnetic field and the wave-vector. Angular distribution of the spectral
density of SMW and Alfv\'en waves (AW) created by turbulent regions and passing
through large regions of partially ionized plasma is qualitatively considered.
The calculated damping rate is expressed by the electron impact cross section
of the hydrogen atom and in short all details of the proposed damping
mechanisms are well studied. | 2005.07730v1 |
2020-07-02 | Uniformly-Damped Binomial Filters: Five-percent Maximum Overshoot Optimal Response Design | In this paper, the five-percent maximum overshoot design of uniformly-damped
binomial filters (transfer-functions) is introduced. First, the butterworth
filter response is represented as a damped-binomial filter response. To extend
the maximum-overshoot response of the second-order butterworth to higher
orders, the binomial theorem is extended to the uniformly-damped binomial
theorem. It is shown that the five-percent uniformly-damped binomial filter is
a compromise between the butterworth filter and the standard binomial filter,
with respect to the filter-approximation problem in the time and frequency
domain. Finally, this paper concludes that in applications of interest, such as
step-tracking, where both strong filtering and a fast, smooth
transient-response, with negligible overshoot are desired, the response of the
normalized five-percent uniformly-damped binomial form is a candidate
replacement for both the butterworth and standard binomial filter forms. | 2007.00890v3 |
2020-09-17 | Temperature Dependent Non-linear Damping in Palladium Nano-mechanical Resonators | Advances in nano-fabrication techniques has made it feasible to observe
damping phenomena beyond the linear regime in nano-mechanical systems. In this
work, we report cubic non-linear damping in palladium nano-mechanical
resonators. Nano-scale palladium beams exposed to a $H_2$ atmosphere become
softer and display enhanced Duffing non-linearity as well as non-linear damping
at ultra low temperatures. The damping is highest at the lowest temperatures of
$\sim 110\: mK$ and decreases when warmed up-to $\sim 1\textrm{ }K$. We
experimentally demonstrate for the first time a temperature dependent
non-linear damping in a nano-mechanical system below 1 K. It is consistent with
a predicted two phonon mediated non-linear Akhiezer scenario for ballistic
phonons with mean free path comparable to the beam thickness. This opens up new
possibilities to engineer non-linear phenomena at low temperatures. | 2009.08324v1 |
2020-12-25 | Information constraint in open quantum systems | We propose an effect called information constraint which is characterized by
the existence of different decay rates of signal strengths propagating along
opposite directions. It is an intrinsic property of a type of open quantum
system, which does not rely on boundary conditions. We define the value of
information constraint ($I_C$) as the ratio of different decay rates and derive
the analytical representation of $I_C$ for general quadratic Lindbladian
systems. Based on information constraint, we can provide a simple and elegant
explanation of chiral and helical damping, and get the local maximum points of
relative particle number for the periodical boundary system, consistent with
numerical calculations. Inspired by information constraint, we propose and
prove the correspondence between edge modes and damping modes. A new damping
mode called Dirac damping is constructed, and chiral/helical damping can be
regarded as a special case of Dirac damping. | 2012.13583v3 |
2021-04-29 | Non-linear damping of standing kink waves computed with Elsasser variables | In a previous paper, we computed the energy density and the non-linear energy
cascade rate for transverse kink waves using Elsasser variables. In this paper,
we focus on the standing kink waves, which are impulsively excited in coronal
loops by external perturbations. We present an analytical calculation to
compute the damping time due to the non-linear development of the
Kelvin-Helmholtz instability. The main result is that the damping time is
inversely proportional to the oscillation amplitude. We compare the damping
times from our formula with the results of numerical simulations and
observations. In both cases we find a reasonably good match. The comparison
with the simulations show that the non-linear damping dominates in the high
amplitude regime, while the low amplitude regime shows damping by resonant
absorption. In the comparison with the observations, we find a power law
inversely proportional to the amplitude $\eta^{-1}$ as an outer envelope for
our Monte Carlo data points. | 2104.14331v1 |
2021-05-31 | Revisiting the Plasmon Radiation Damping of Gold Nanorods | Noble metal nanoparticles have been utilized for a vast amount of optical
applications. For the applications that used metal nanoparticles as nanosensors
and optical labeling, larger radiation damping is preferred (higher optical
signal). To get a deeper knowledge about the radiation damping of noble metal
nanoparticles, we used gold nanorods with different geometry factors (aspect
ratios) as the model system to study. We investigated theoretically how the
radiation damping of a nanorod depends on the material, and shape of the
particle. Surprisingly, a simple analytical equation describes radiation
damping very accurately and allow to disentangle the maximal radiation damping
parameter for gold nanorod with resonance energy E_res around 1.81 eV (685 nm).
We found very good agreement with theoretical predictions and experimental data
obtained by single-particle spectroscopy. Our results and approaches may pave
the way for designing and optimizing gold nanostructure with higher optical
signal and better sensing performance. | 2105.14873v1 |
2021-06-23 | Bayesian evidence for a nonlinear damping model for coronal loop oscillations | Recent observational and theoretical studies indicate that the damping of
solar coronal loop oscillations depends on the oscillation amplitude. We
consider two mechanisms, linear resonant absorption and a nonlinear damping
model. We confront theoretical predictions from these models with observed data
in the plane of observables defined by the damping ratio and the oscillation
amplitude. The structure of the Bayesian evidence in this plane displays a
clear separation between the regions where each model is more plausible
relative to the other. There is qualitative agreement between the regions of
high marginal likelihood and Bayes factor for the nonlinear damping model and
the arrangement of observed data. A quantitative application to 101 loop
oscillation cases observed with SDO/AIA results in the marginal likelihood for
the nonlinear model being larger in the majority of them. The cases with
conclusive evidence for the nonlinear damping model outnumber considerably
those in favor of linear resonant absorption. | 2106.12243v1 |
2021-07-13 | Convergence of iterates for first-order optimization algorithms with inertia and Hessian driven damping | In a Hilbert space setting, for convex optimization, we show the convergence
of the iterates to optimal solutions for a class of accelerated first-order
algorithms. They can be interpreted as discrete temporal versions of an
inertial dynamic involving both viscous damping and Hessian-driven damping. The
asymptotically vanishing viscous damping is linked to the accelerated gradient
method of Nesterov while the Hessian driven damping makes it possible to
significantly attenuate the oscillations. By treating the Hessian-driven
damping as the time derivative of the gradient term, this gives, in discretized
form, first-order algorithms. These results complement the previous work of the
authors where it was shown the fast convergence of the values, and the fast
convergence towards zero of the gradients. | 2107.05943v1 |
2021-12-13 | Effect of interfacial damping on high-frequency surface wave resonance on a nanostrip-bonded substrate | Since surface acoustic waves (SAW) are often generated on substrates to which
nanostrips are periodically attached, it is very important to consider the
effect of interface between the deposited strip and the substrate surface,
which is an unavoidable issue in manufacturing. In this paper, we propose a
theoretical model that takes into account the interface damping and calculate
the dispersion relationships both for frequency and attenuation of SAW
resonance. This results show that the interface damping has an insignificant
effect on resonance frequency, but, interestingly, attenuation of the SAW can
decrease significantly in the high frequency region as the interface damping
increases. Using picosecond ultrasound spectroscopy, we confirm the validity of
our theory; the experimental results show similar trends both for resonant
frequency and attenuation in the SAW resonance. Furthermore, the resonant
behavior of the SAW is simulated using the finite element method, and the
intrinsic cause of interface damping on the vibrating system is discussed.
These findings strongly indicate the necessity of considering interfacial
damping in the design of SAW devices. | 2112.06367v1 |
2022-09-13 | Latest results from the DAMPE space mission | The DArk Matter Particle Explorer (DAMPE) is a space-based particle detector
launched on December 17th, 2015 from the Jiuquan Satellite Launch Center
(China). The main goals of the DAMPE mission are the study of galactic cosmic
rays (CR), the electron-positron energy spectrum, gamma-ray astronomy, and
indirect dark matter search. Among its sub-detectors, the deep calorimeter
makes DAMPE able to measure electrons and gamma-ray spectra up to 10 TeV, and
CR nuclei spectra up to hundreds of TeV, with unprecedented energy resolution.
This high-energy region is important in order to search for electron-positron
sources, for dark matter signatures in space, and to clarify CR acceleration
and propagation mechanisms inside our galaxy. A general overview of the DAMPE
experiment will be presented in this work, along with its main results and
ongoing activities. | 2209.06014v1 |
2022-10-25 | Microscopic structure of electromagnetic whistler wave damping by kinetic mechanisms in hot magnetized Vlasov plasmas | The kinetic damping mechanism of low frequency transverse perturbations
propagating parallel to the magnetic field in a magnetized warm electron plasma
is simulated by means of electromagnetic (EM) Vlasov simulations. The
short-time-scale damping of the electron magnetohydrodynamic whistler
perturbations and underlying physics of finite electron temperature effect on
its real frequency are recovered rather deterministically, and analyzed. The
damping arises from an interplay between a global (prevailing over entire
phase-space) and the more familiar resonant-electron-specific kinetic damping
mechanisms, both of which preserve entropy but operate distinctly by leaving
their characteristic signatures on an initially coherent finite amplitude
modification of the warm electron equilibrium distribution. The net damping
results from a deterministic thermalization, or phase-mixing process, largely
supplementing the resonant acceleration of electrons at shorter time scales,
relevant to short-lived turbulent EM fluctuations. A kinetic model for the
evolving initial transverse EM perturbation is presented and applied to
signatures of the whistler wave phase-mixing process in simulations. | 2210.13764v1 |
2023-01-13 | An artificially-damped Fourier method for dispersive evolution equations | Computing solutions to partial differential equations using the fast Fourier
transform can lead to unwanted oscillatory behavior. Due to the periodic nature
of the discrete Fourier transform, waves that leave the computational domain on
one side reappear on the other and for dispersive equations these are typically
high-velocity, high-frequency waves. However, the fast Fourier transform is a
very efficient numerical tool and it is important to find a way to damp these
oscillations so that this transform can still be used. In this paper, we
accurately model solutions to four nonlinear partial differential equations on
an infinite domain by considering a finite interval and implementing two
damping methods outside of that interval: one that solves the heat equation and
one that simulates rapid exponential decay. Heat equation-based damping is best
suited for small-amplitude, high-frequency oscillations while exponential decay
is used to damp traveling waves and high-amplitude oscillations. We demonstrate
significant improvements in the runtime of well-studied numerical methods when
adding in the damping method. | 2301.05789v1 |
2023-03-07 | Stabilization of the wave equation on larger-dimension tori with rough dampings | This paper deals with uniform stabilization of the damped wave equation. When
the manifold is compact and the damping is continuous, the geometric control
condition is known to be necessary and sufficient. In the case where the
damping is a sum of characteristic functions of polygons on a two-dimensional
torus, a result by Burq-G\'erard states that stabilization occurs if and only
if every geodesic intersects the interior of the damped region or razes damped
polygons on both sides. We give a natural generalization of their result to a
sufficient condition on tori of any dimension $d \geq 3$. In some particular
cases, we show that this sufficient condition can be weakened. | 2303.03733v4 |
2023-07-10 | The Characteristic Shape of Damping Wings During Reionization | Spectroscopic analysis of Ly$\alpha$ damping wings of bright sources at $z>6$
is a promising way to measure the reionization history of the universe.
However, the theoretical interpretation of the damping wings is challenging due
to the inhomogeneous nature of the reionization process and the proximity
effect of bright sources. In this Letter, we analyze the damping wings arising
from the neutral patches in the radiative transfer cosmological simulation
suite Cosmic Reionization on Computers (CROC). We find that the damping wing
profile remains a tight function of volume-weighted neutral fraction $\left<
x_{\rm HI} \right>_{\rm v}$, especially when $\left< x_{\rm HI} \right>_{\rm
v}>0.5$, despite the patchy nature of reionization and the proximity effect.
This small scatter indicates that with a well-measured damping wing profile, we
could constrain the volume-weighted neutral fraction as precise as $\Delta
\left< x_{\rm HI} \right>_{\rm v} \lesssim 0.1$ in the first half of
reionization. | 2307.04797v1 |
2023-07-17 | Dissipation in solids under oscillatory shear: Role of damping scheme and sample thickness | We study dissipation as a function of sample thickness in solids under global
oscillatory shear applied to the top layer of the sample. Two types of damping
mechanism are considered: Langevin and Dissipative Particle Dynamics (DPD). In
the regime of low driving frequency, and under strain-controlled conditions, we
observe that for Langevin damping, dissipation increases with sample thickness,
while for DPD damping, it decreases. Under force-controlled conditions,
dissipation increases with sample thickness for both damping schemes. These
results can be physically understood by treating the solid as a one-dimensional
harmonic chain in the quasi-static limit, for which explicit equations (scaling
relations) describing dissipation as a function of chain length (sample
thickness) are provided. The consequences of these results, in particular
regarding the choice of damping scheme in computer simulations, are discussed. | 2307.08413v1 |
2023-08-17 | A low-rank algorithm for strongly damped wave equations with visco-elastic damping and mass terms | Damped wave equations have been used in many real-world fields. In this
paper, we study a low-rank solution of the strongly damped wave equation with
the damping term, visco-elastic damping term and mass term. Firstly, a
second-order finite difference method is employed for spatial discretization.
Then, we receive a second-order matrix differential system. Next, we transform
it into an equivalent first-order matrix differential system, and split the
transformed system into three subproblems. Applying a Strang splitting to these
subproblems and combining a dynamical low-rank approach, we obtain a low-rank
algorithm. Numerical experiments are reported to demonstrate that the proposed
low-rank algorithm is robust and accurate, and has second-order convergence
rate in time. | 2308.08888v2 |
2023-10-30 | Optimal backward uniqueness and polynomial stability of second order equations with unbounded damping | For general second order evolution equations, we prove an optimal condition
on the degree of unboundedness of the damping, that rules out finite-time
extinction. We show that control estimates give energy decay rates that
explicitly depend on the degree of unboundedness, and establish a dilation
method to turn existing control estimates for one propagator into those for
another in the functional calculus. As corollaries, we prove Schr\"odinger
observability gives decay for unbounded damping, weak monotonicity in damping,
and quantitative unique continuation and optimal propagation for fractional
Laplacians. As applications, we establish a variety of novel and explicit
energy decay results to systems with unbounded damping, including singular
damping, linearised gravity water waves and Euler--Bernoulli plates. | 2310.19911v1 |
2024-03-12 | Modulational instability of nonuniformly damped, broad-banded waves: applications to waves in sea-ice | This paper sets out to explore the modulational (or Benjamin-Feir)
instability of a monochromatic wave propagating in the presence of damping such
as that induced by sea-ice on the ocean surface. The fundamental wave motion is
modelled using the spatial Zakharov equation, to which either uniform or
non-uniform (frequency dependent) damping is added. By means of mode truncation
the spatial analogue of the classical Benjamin-Feir instability can be studied
analytically using dynamical systems techniques. The formulation readily yields
the free surface envelope, giving insight into the physical implications of
damping on the modulational instability. The evolution of an initially unstable
mode is also studied numerically by integrating the damped, spatial Zakharov
equation, in order to complement the analytical theory. This sheds light on the
effects of damping on spectral broadening arising from this instability. | 2403.07425v1 |
1994-05-12 | Black Hole Relics and Inflation: Limits on Blue Perturbation Spectra | Blue primordial power spectra have spectral index $n>1$ and arise naturally
in the recently proposed hybrid inflationary scenario. An observational upper
limit on {\em n} is derived by normalizing the spectrum at the quadrupole scale
and considering the possible overproduction of Planck mass relics formed in the
final stage of primordial black hole evaporation. In the inflationary Universe
with the maximum reheating temperature compatible with the observed quadrupole
anisotropy, the upper limit is $n=1.4$, but it is slightly weaker for lower
reheat temperatures. This limit applies over 57 decades of mass and is
therefore insensitive to cosmic variance and any gravitational wave
contribution to the quadrupole anisotropy. It is also independent of the dark
matter content of the Universe and therefore the bias parameter. In some
circumstances, there may be an extended dust-like phase between the end of
inflation and reheating. In this case, primordial black holes form more
abundantly and the upper limit is $n=1.3$. | 9405027v1 |
1995-02-01 | Spectra and Statistics of Cosmic String Perturbations on the Microwave Background: A Monte Carlo Approach | Using Monte Carlo simulations of perturbations induced by cosmic strings on
the microwave background, we demonstrate the scale invariance of string
fluctuation patterns. By comparing string-induced fluctuation patterns with
gaussian random phase ones, we show that the non-gaussian signatures of the
string patterns are detectable by tests based on the moments of the
distributions only for angular scales smaller than a few arcminutes and for
maps based on the gradient of temperature fluctuations. However, we find that
tests of the gaussianity of the moments fail when we include a reasonable
amount of instrumental noise in a pattern. Signal to noise ratios of $3.3$ or
greater completely suppress a string pattern's non-gaussian features even at
the highest resolutions. | 9502004v2 |
1999-04-16 | The Sunyaev-Zeldovich Effect as Microwave Foreground and Probe of Cosmology | The Sunyaev-Zel'dovich (SZ) effect from clusters of galaxies should yield a
significant signal in cosmic microwave background(CMB) experiments at small
angular scales ($\ell \ga 1000$). Experiments with sufficient frequency
coverage should be able to remove much of this signal in order to recover the
primary anisotropy. The SZ signal is interesting in its own right; the
amplitude and angular dependence are sensitive to both cosmology and the
evolution of the gas. Combining CMB measurements with planned non-targeted SZ
surveys could isolate the cosmological effects, providing CMB experiments with
a low-redshift test of cosmology as a consistency check. Improvements in the
determination of the angular diameter distance as a function of redshift from
SZ and X-ray observations of a large sample of clusters will also provide a
probe of cosmology. | 9904220v1 |
2000-12-05 | Near-IR Spectroscopy and Population Synthesis of Super Star Clusters in NGC 1569 | We present H- and K-band NIRSPEC spectroscopy of super star clusters (SSCs)
in the irregular starburst galaxy NGC 1569, obtained at the Keck Observatory.
We fit these photospheric spectra to NextGen model atmospheres to obtain
effective spectral types of clusters, and find that the information in both H-
and K-band spectra is necessary to remove degeneracy in the fits. The light of
SSC B is unambiguously dominated by K0 supergiants (T_eff=4400 +- 100 K, log
g=0.5 +- 0.5). The double cluster SSC A has higher T_eff (G5) and less tightly
constrained surface gravity (log g=1.3 +- 1.3), consistent with a mixed stellar
population dominated by blue Wolf-Rayet stars and red supergiants. We predict
the time evolution of infrared spectra of SSCs using Starburst99 population
synthesis models coupled with empirical stellar spectral libraries (at solar
metallicity). The resulting model sequence allows us to assign ages of 15-18
Myr for SSC B and 18-21 Myr for SSC A. | 0012089v1 |
2001-05-14 | Understanding Cluster Gas Evolution and Fine-Scale CMB Anisotropy with Deep Sunyaev-Zel'dovich Effect Surveys | We investigate the impact of gas evolution on the expected yields from deep
Sunyaev-Zel'dovich (SZ) effect surveys as well as on the expected SZ effect
contribution to fine scale anisotropy in the Cosmic Microwave Background. The
approximate yields from SZ effect surveys are remarkably insensitive to gas
evolution, even though the observable properties of the resulting clusters can
be markedly different. The CMB angular power spectrum at high multipoles due to
the SZ effect from clusters is quite sensitive to gas evolution. We show that
moderate resolution SZ effect imaging of clusters found in deep SZ effect
surveys should allow a good understanding of gas evolution in galaxy clusters,
independent of the details of the nature of the gas evolution. Such an
understanding will be necessary before precise cosmological constraints can be
set from yields of large cluster surveys. | 0105229v1 |
2001-05-22 | Constraints on Omega_m, Omega_L, and Sigma_8, from Galaxy Cluster Redshift Distributions | We show that the counts of galaxy clusters in future deep cluster surveys can
place strong constraints on the matter density, Omega_m, the vacuum energy
density, Omega_L, and the normalization of the matter power spectrum, sigma_8.
Degeneracies between these parameters are different from those in studies of
either high--redshift type Ia Supernovae (SNe), or cosmic microwave background
(CMB) anisotropies. Using a mass threshold for cluster detection expected to be
typical for upcoming SZE surveys, we find that constraints on Omega_m and
sigma_8 at the level of roughly 5% or better can be expected, assuming redshift
information is known at least to z=0.5 and in the absence of significant
systematic errors. Without information past this redshift, Omega_L is
constrained to 25%. With complete redshift information, deep (M_{lim}=
10^{14}h^{-1}{M_sun}), relatively small solid angle (roughly 12 {deg}^2)
surveys can further constrain Omega_L to an accuracy of 15%, while large solid
angle surveys with ground-based large-format bolometer arrays could measure
Omega_L to a precision of 4% or better. | 0105396v2 |
2002-05-27 | Radio Point Sources and the Thermal SZ Power Spectrum | Radio point sources are strongly correlated with clusters of galaxies, so a
significant fraction of the thermal Sunyaev-Zel'dovich (SZ) effect signal could
be affected by point source contamination. Based on empirical estimates of the
radio galaxy population, it is shown that the rms temperature fluctuations of
the thermal SZ effect could be underestimated by as much as 30% at an observing
frequency of 30 GHz at l>1000. The effect is larger at higher multipoles. If
the recent report of excess power at small angular scales is to be explained by
the thermal SZ effect, then radio point sources at an observing frequency of 30
GHz must be a surprisingly weak contaminant of the SZ effect for low-mass
clusters. | 0205467v2 |
2002-07-29 | Measuring Cluster Peculiar Velocities and Temperatures at cm and mm Wavelengths | We present a detailed investigation of issues related to the measurement of
peculiar velocities and temperatures using Sunyaev-Zel'dovich (SZ) effects. We
estimate the accuracy to which peculiar velocities and gas temperatures of
distant galaxy clusters could be measured. With uK sensitivity on arcminute
scales at several frequencies it will be possible to measure peculiar
velocities to an accuracy of about 130 km/s and gas temperatures to better than
1 keV. The limiting factor for the accuracy of the measured peculiar velocity
is the presence of bulk motions within the galaxy cluster, even for apparently
relaxed clusters. The accuracy of the temperature is mainly limited by noise.
These results are independent of redshift. Such constraints can best be
achieved with only three frequencies: one in the Rayleigh-Jeans region (<40
GHz), one near 150 GHz, and the third at 300 GHz or higher. Measurements at the
null of the thermal SZ effect are of marginal utility, other than as a
foreground/background monitor. | 0207600v2 |
2002-07-29 | CMB-Normalized Predictions for Sunyaev-Zel'dovich effect fluctuations | We predict the level of small-scale anisotropy in the cosmic microwave
background (CMB) due to the Sunyaev--Zel'dovich (SZ) effect for the ensemble of
cosmological models that are consistent with current measurements of
large-scale CMB anisotropy. We argue that the recently reported detections of
the small-scale (arcminutes) CMB anisotropy are only marginally consistent with
being the SZ effect when cosmological models are calibrated to the existing
primary CMB data on large scales. The discrepancy is at more than 2-2.5 sigma,
and is mainly due to a lower sigma_8 <0.8 favored by the primary CMB and a
higher sigma_8 > 1 favored by the SZ effect. A degeneracy between the optical
depth to Thomson scattering and the CMB-derived value of sigma_8 suggests that
the discrepancy is reduced if the universe was reionized very early, at a
redshift of about 25. | 0207633v1 |
2002-08-08 | Cosmology with the Sunyaev-Zel'dovich Effect | The Sunyaev-Zel'dovich effect (SZE) provides a unique way to map the
large-scale structure of the universe as traced by massive clusters of
galaxies. As a spectral distortion of the cosmic microwave background, the SZE
is insensitive to the redshift of the galaxy cluster, making it well-suited for
studies of clusters at all redshifts, and especially at reasonably high
redshifts (z > 1) where the abundance of clusters is critically dependent on
the underlying cosmology. Recent high signal-to-noise detections of the SZE
have enabled interesting constraints on the Hubble constant and the matter
density of the universe using small samples of galaxy clusters. Upcoming SZE
surveys are expected to find hundreds to thousands of new galaxy clusters, with
a mass selection function that is remarkably uniform with redshift. In this
review we provide an overview of the SZE and its use for cosmological studies
with emphasis on the cosmology that can, in principle, be extracted from SZE
survey yields. We discuss the observational and theoretical challenges that
must be met before precise cosmological constraints can be extracted from the
survey yields. | 0208192v1 |
2002-09-25 | External Shear in Quadruply Imaged Lens Systems | We use publicly available N-body simulations and semi-analytic models of
galaxy formation to estimate the levels of external shear due to structure near
the lens in gravitational lens systems. We also describe two selection effects,
specific to four-image systems, that enhance the probability of observing
systems to have higher external shear. Ignoring additional contributions from
"cosmic shear" and assuming that lens galaxies are not significantly flattened,
we find that the mean shear at the position of a quadruple lens galaxy is 0.11,
the rms shear is roughly 0.15, and there is roughly a 45% likelihood of
external shear greater than 0.1. This is much larger than previous estimates
and in good agreement with typical measured external shear. The higher shear
primarily stems from the tendency of early-type galaxies, which are the
majority of lenses, to reside in overdense regions. | 0209532v2 |
2003-05-21 | A Method for Mapping the Temperature Profile of X-ray Clusters Through Radio Observations | Many of the most luminous extragalactic radio sources are located at the
centers of X-ray clusters, and so their radiation must be scattered by the
surrounding hot gas. We show that radio observations of the highly-polarized
scattered radiation (which depends on the electron density distribution) in
combination with the thermal Sunyaev-Zeldovich effect (which measures the
electron pressure distribution), can be used to determine the radial profile of
the electron temperature within the host cluster. The sensitivity levels
expected from current instruments will allow radio measurements of
mass-weighted cluster temperature profiles to better than roughly 1 keV
accuracy, as long as the central radio source is steady over several million
years. Variable or beamed sources will leave observable signatures in the
scattered emission. For clusters with a central point source brighter than
about 1 mJy, the scattered polarization signal is stronger than competing
effects due to the cosmic microwave background. | 0305417v1 |
2006-09-26 | Reconstructing the Thomson Optical Depth due to Patchy Reionization with 21-cm Fluctuation Maps | Large fluctuations in the electron column density can occur during the
reionization process. We investigate the possibility of deriving the electron
density fluctuations through detailed mapping of the redshifted 21-cm emission
from the neutral medium during reionization. We find that the
electron-scattering optical depth and 21-cm differential brightness temperature
are strongly anti-correlated, allowing optical depth estimates based entirely
on redshifted 21-cm measurements. This should help isolate the CMB polarization
fluctuations that are due to reionization, allowing both cleaning of the patchy
reionization polarization signal as a contaminating source of confusion to
other signals and a measurement of the primordial quadrupole that would be
measured at various locations in the universe at the epoch of reionization.
This latter application in principle allows mapping of the primordial density
field at z~1100 over a large fraction of the Hubble volume. | 0609689v2 |
1998-07-06 | Field Driven Thermostated System : A Non-Linear Multi-Baker Map | In this paper, we discuss a simple model for a field driven, thermostated
random walk that is constructed by a suitable generalization of a multi-baker
map. The map is a usual multi-baker, but perturbed by a thermostated external
field that has many of the properties of the fields used in systems with
Gaussian thermostats. For small values of the driving field, the map is
hyperbolic and has a unique SRB measure that we solve analytically to first
order in the field parameter. We then compute the positive and negative
Lyapunov exponents to second order and discuss their relation to the transport
properties. For higher values of the parameter, this system becomes
non-hyperbolic and posseses an attractive fixed point. | 9807011v2 |
2006-01-19 | Fluctuation theorem for constrained equilibrium systems | We discuss the fluctuation properties of equilibrium chaotic systems with
constraints such as iso-kinetic and Nos\'e-Hoover thermostats. Although the
dynamics of these systems does not typically preserve phase-space volumes, the
average phase-space contraction rate vanishes, so that the stationary states
are smooth. Nevertheless finite-time averages of the phase-space contraction
rate have non-trivial fluctuations which we show satisfy a simple version of
the Gallavotti-Cohen fluctuation theorem, complementary to the usual
fluctuation theorem for non-equilibrium stationary states, and appropriate to
constrained equilibrium states. Moreover we show these fluctuations are
distributed according to a Gaussian curve for long-enough times. Three
different systems are considered here, namely (i) a fluid composed of particles
interacting with Lennard-Jones potentials; (ii) a harmonic oscillator with
Nos\'e-Hoover thermostatting; (iii) a simple hyperbolic two-dimensional map. | 0601435v1 |
2003-06-12 | ATLAS Data Challenge 1 | In 2002 the ATLAS experiment started a series of Data Challenges (DC) of
which the goals are the validation of the Computing Model, of the complete
software suite, of the data model, and to ensure the correctness of the
technical choices to be made. A major feature of the first Data Challenge (DC1)
was the preparation and the deployment of the software required for the
production of large event samples for the High Level Trigger (HLT) and physics
communities, and the production of those samples as a world-wide distributed
activity. The first phase of DC1 was run during summer 2002, and involved 39
institutes in 18 countries. More than 10 million physics events and 30 million
single particle events were fully simulated. Over a period of about 40 calendar
days 71000 CPU-days were used producing 30 Tbytes of data in about 35000
partitions. In the second phase the next processing step was performed with the
participation of 56 institutes in 21 countries (~ 4000 processors used in
parallel). The basic elements of the ATLAS Monte Carlo production system are
described. We also present how the software suite was validated and the
participating sites were certified. These productions were already partly
performed by using different flavours of Grid middleware at ~ 20 sites. | 0306052v1 |
2004-06-21 | Long Nonbinary Codes Exceeding the Gilbert - Varshamov Bound for any Fixed Distance | Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance
d. We study the minimum asymptotic redundancy \rho(q,n,d)=n-log_q A(q,n,d) as n
grows while q and d are fixed. For any d and q<=d-1, long algebraic codes are
designed that improve on the BCH codes and have the lowest asymptotic
redundancy \rho(q,n,d) <= ((d-3)+1/(d-2)) log_q n known to date. Prior to this
work, codes of fixed distance that asymptotically surpass BCH codes and the
Gilbert-Varshamov bound were designed only for distances 4,5 and 6. | 0406039v3 |
2006-08-19 | Algorithmic linear dimension reduction in the l_1 norm for sparse vectors | This paper develops a new method for recovering m-sparse signals that is
simultaneously uniform and quick. We present a reconstruction algorithm whose
run time, O(m log^2(m) log^2(d)), is sublinear in the length d of the signal.
The reconstruction error is within a logarithmic factor (in m) of the optimal
m-term approximation error in l_1. In particular, the algorithm recovers
m-sparse signals perfectly and noisy signals are recovered with polylogarithmic
distortion. Our algorithm makes O(m log^2 (d)) measurements, which is within a
logarithmic factor of optimal. We also present a small-space implementation of
the algorithm. These sketching techniques and the corresponding reconstruction
algorithms provide an algorithmic dimension reduction in the l_1 norm. In
particular, vectors of support m in dimension d can be linearly embedded into
O(m log^2 d) dimensions with polylogarithmic distortion. We can reconstruct a
vector from its low-dimensional sketch in time O(m log^2(m) log^2(d)).
Furthermore, this reconstruction is stable and robust under small
perturbations. | 0608079v1 |
2007-03-06 | LIBOPT - An environment for testing solvers on heterogeneous collections of problems - Version 1.0 | The Libopt environment is both a methodology and a set of tools that can be
used for testing, comparing, and profiling solvers on problems belonging to
various collections. These collections can be heterogeneous in the sense that
their problems can have common features that differ from one collection to the
other. Libopt brings a unified view on this composite world by offering, for
example, the possibility to run any solver on any problem compatible with it,
using the same Unix/Linux command. The environment also provides tools for
comparing the results obtained by solvers on a specified set of problems. Most
of the scripts going with the Libopt environment have been written in Perl. | 0703025v1 |
1995-09-19 | Harmonic Maps with Prescribed Singularities on Unbounded Domains | The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and
axially symmetric case to a harmonic map with prescribed singularities
$\p\colon\R^3\sm\Sigma\to\H^{k+1}_\C$ into the $(k+1)$-dimensional complex
hyperbolic space. In this paper, we prove the existence and uniqueness of
harmonic maps with prescribed singularities $\p\colon\R^n\sm\Sigma\to\H$, where
$\Sigma$ is an unbounded smooth closed submanifold of $\R^n$ of codimension at
least $2$, and $\H$ is a real, complex, or quaternionic hyperbolic space. As a
corollary, we prove the existence of solutions to the reduced stationary and
axially symmetric Einstein/Abelian-Yang-Mills Equations. | 9509003v1 |
1994-12-12 | N-Black Hole Stationary and Axially Symmetric Solutions of the Einstein-Maxwell Equations | The Einstein/Maxwell equations reduce in the stationary and axially symmetric
case to a harmonic map with prescribed singularities phi: R^3\Sigma -> H^2_C,
where Sigma is a subset of the axis of symmetry, and H^2_C is the complex
hyperbolic plane. Motivated by this problem, we prove the existence and
uniqueness of harmonic maps with prescribed singularities phi: R^n\Sigma -> H,
where Sigma is a submanifold of R^n of co-dimension at least 2, and H is a
classical Riemannian globally symmetric space of noncompact type and rank one.
This result, when applied to the black hole problem, yields solutions which can
be interpreted as equilibrium configurations of multiple co-axially rotating
charged black holes held apart by singular struts. | 9412036v2 |
1997-11-17 | Novel Electroweak Symmetry Breaking Conditions From Quantum Effects In The MSSM | We present, in the context of the Minimal Supersymmetric Standard Model, a
detailed one-loop analytic study of the minimization conditions of the
effective potential in the Higgs sector.
Special emphasis is put on the role played by $Str M^4$ in the determination
of the electroweak symmetry breaking conditions, where first and second order
derivatives of the effective potential are systematically taken into account.
Novel, necessary (and sufficient in the Higgs sector) model-independent
constraints, are thus obtained analytically, leading to new theoretical lower
and upper bounds on $\tan \beta$. Although fully model-independent, these
bounds are found to be much more restrictive than the existing model-dependent
ones! A first illustration is given in the context of a SUGRA-GUT motivated
scenario. | 9711356v1 |
1999-01-08 | On the fourth adjoint Contractions of divisorial and fiber types | In this paper, we will list up all the cases for the ray contractions of
divisorial and fiber types for smooth projective varieties of dimension five.
These are obtained as a corollary from the lists of n-dimensional k-th adjoint
contractions f: X -> Y of the same types for k=1,2,3 and 4 (n> or =5). The
lists for k=1,2 and 3 have previously been obtained in [Na], Proposition 1.2
and Theorem 1.3. The main task will be to have such a list for k=4, where one
case in the list fails to show that a positive-dimensional general fiber F of f
is irreducible when n>5. This assertion will, however, be proven when n=5 with
an essential aid of 3-dimensional Minimal Model Program in [Mo2]. (We do not
show the existence of cases.) | 9901033v2 |
2004-04-19 | Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Binary Codes | Given positive integers $n$ and $d$, let $A_2(n,d)$ denote the maximum size
of a binary code of length $n$ and minimum distance $d$. The well-known
Gilbert-Varshamov bound asserts that $A_2(n,d) \geq 2^n/V(n,d-1)$, where
$V(n,d) = \sum_{i=0}^{d} {n \choose i}$ is the volume of a Hamming sphere of
radius $d$. We show that, in fact, there exists a positive constant $c$ such
that $$ A_2(n,d) \geq c \frac{2^n}{V(n,d-1)} \log_2 V(n,d-1) $$ whenever $d/n
\le 0.499$. The result follows by recasting the Gilbert- Varshamov bound into a
graph-theoretic framework and using the fact that the corresponding graph is
locally sparse. Generalizations and extensions of this result are briefly
discussed. | 0404325v1 |
2005-11-03 | On the automorphism group of generalized Baumslag-Solitar groups | A generalized Baumslag-Solitar group (GBS group) is a finitely generated
group $G$ which acts on a tree with all edge and vertex stabilizers infinite
cyclic. We show that Out(G) either contains non-abelian free groups or is
virtually nilpotent of class at most 2. It has torsion only at finitely many
primes.
One may decide algorithmically whether Out(G) is virtually nilpotent or not.
If it is, one may decide whether it is virtually abelian, or finitely
generated. The isomorphism problem is solvable among GBS groups with Out(G)
virtually nilpotent.
If $G$ is unimodular (virtually $F_n \times Z$), then Out(G) is commensurable
with a semi-direct product $Z^k \rtimes Out(H)$ with $H$ virtually free. | 0511083v1 |
2001-07-08 | Statistically Preserved Structures in Shell Models of Passive Scalar Advection | It was conjectured recently that Statiscally Preserved Structures underlie
the statistical physics of turbulent transport processes. We analyze here in
detail the time-dependent (non compact) linear operator that governs the
dynamics of correlation functions in the case of shell models of passive scalar
advection. The problem is generic in the sense that the driving velocity field
is neither Gaussian nor $\delta$-correlated in time. We show how to naturally
discuss the dynamics in terms of an effective compact operator that displays
"zero modes" which determine the anomalous scaling of the correlation
functions. Since shell models have neither Lagrangian structure nor "shape
dynamics" this example differs significantly from standard passive scalar
advection. Nevertheless with the necessary modifications the generality and
efficacy of the concept of Statistically Preserved Structures are further
exemplified. In passing we point out a bonus of the present approach, in
providing analytic predictions for the time-dependent correlation functions in
decaying turbulent transport. | 0107016v1 |
2001-11-13 | Statistically Preserved Structures and Anomalous Scaling in Turbulent Active Scalar Advection | The anomalous scaling of correlation functions in the turbulent statistics of
active scalars (like temperature in turbulent convection) is understood in
terms of an auxiliary passive scalar which is advected by the same turbulent
velocity field. While the odd-order correlation functions of the active and
passive fields differ, we propose that the even-order correlation functions are
the same to leading order (up to a trivial multiplicative factor). The leading
correlation functions are statistically preserved structures of the passive
scalar decaying problem, and therefore universality of the scaling exponents of
the even-order correlations of the active scalar is demonstrated. | 0111030v1 |
2003-03-27 | On the parametric dependences of a class of non-linear singular maps | We discuss a two-parameter family of maps that generalize piecewise linear,
expanding maps of the circle. One parameter measures the effect of a
non-linearity which bends the branches of the linear map. The second parameter
rotates points by a fixed angle. For small values of the nonlinearity
parameter, we compute the invariant measure and show that it has a singular
density to first order in the nonlinearity parameter. Its Fourier modes have
forms similar to the Weierstrass function. We discuss the consequences of this
singularity on the Lyapunov exponents and on the transport properties of the
corresponding multibaker map. For larger non-linearities, the map becomes
non-hyperbolic and exhibits a series of period-adding bifurcations. | 0303062v1 |
2001-06-06 | The Secrecy Capacity of Practical Quantum Cryptography | Quantum cryptography has attracted much recent attention due to its potential
for providing secret communications that cannot be decrypted by any amount of
computational effort. This is the first analysis of the secrecy of a practical
implementation of the BB84 protocol that simultaneously takes into account and
presents the {\it full} set of complete analytical expressions for effects due
to the presence of pulses containing multiple photons in the attenuated output
of the laser, the finite length of individual blocks of key material, losses
due to error correction, privacy amplification, continuous authentication,
errors in polarization detection, the efficiency of the detectors, and
attenuation processes in the transmission medium. The analysis addresses
eavesdropping attacks on individual photons rather than collective attacks in
general. Of particular importance is the first derivation of the necessary and
sufficient amount of privacy amplification compression to ensure secrecy
against the loss of key material which occurs when an eavesdropper makes
optimized individual attacks on pulses containing multiple photons. It is shown
that only a fraction of the information in the multiple photon pulses is
actually lost to the eavesdropper. | 0106033v1 |
2005-11-17 | Quantum Computer Condition: Stability, Classical Computation and Norms | The Quantum Computer Condition (QCC) provides a rigorous and completely
general framework for carrying out analyses of questions pertaining to
fault-tolerance in quantum computers. In this paper we apply the QCC to the
problem of fluctuations and systematic errors in the values of characteristic
parameters in realistic systems. We show that fault-tolerant quantum
computation is possible despite variations in these parameters. We also use the
QCC to explicitly show that reliable classical computation can be carried out
using as input the results of fault-tolerant, but imperfect, quantum
computation. Finally, we consider the advantages and disadvantages of the
superoperator and diamond norms in connection with application of the QCC to
various quantum information-theoretic problems. | 0511177v1 |
2006-12-19 | On the use of photonic N00N states for practical quantum interferometry | The performance of photonic $N00N$ states, propagating in an attenuating
medium, is analyzed with respect to phase estimation. It is shown that, for
$N00N$ states propagating through a lossy medium, the Heisenberg limit is never
achieved. It is also shown that, for a given value of $N$, a signal comprised
of an attenuated separable state of $N$ photons will actually produce a better
phase estimate than will a signal comprised of an equally attenuated $N00N$
state, unless the transmittance of the medium is very high. This is a
consequence of the need to utilize measurement operators appropriate to the
different signal states. The result is that, for most practical applications in
realistic scenarios with attenuation, the resolution of $N00N$ state-based
phase estimation not only does not achieve the Heisenberg Limit, but is
actually worse than the Standard Quantum Limit. It is demonstrated that this
performance deficit becomes more pronounced as the number, $N$, of photons in
the signal increases. | 0612156v1 |
2007-05-22 | Analysis of evidence of Mars life | Gillevinia straata, the scientific name [1, 2] recognizing the first
extraterrestrial living form ever nomenclated, as well as the existence of a
new biological kingdom, Jakobia, in a new biosphere -Marciana- of what now has
become the living system Solaria, is grounded on old evidence reinterpreted in
the light of newly acquired facts. The present exposition provides a summary
overview of all these grounds, outlined here as follows. A more detailed paper
is being prepared for publication. | 0705.3176v3 |
2007-06-26 | Feedback in the Antennae Galaxies (NGC 4038/9): I. High-Resolution Infrared Spectroscopy of Winds from Super Star Clusters | We present high-resolution (R ~ 24,600) near-IR spectroscopy of the youngest
super star clusters (SSCs) in the prototypical starburst merger, the Antennae
Galaxies. These SSCs are young (3-7 Myr old) and massive (10^5 - 10^7 M_sun for
a Kroupa IMF) and their spectra are characterized by broad, extended Br-gamma
emission, so we refer to them as emission-line clusters (ELCs) to distinguish
them from older SSCs. The Brgamma lines of most ELCs have supersonic widths
(60-110 km/s FWHM) and non-Gaussian wings whose velocities exceed the clusters'
escape velocities. This high-velocity unbound gas is flowing out in winds that
are powered by the clusters' massive O and W-R stars over the course of at
least several crossing times. The large sizes of some ELCs relative to those of
older SSCs may be due to expansion caused by these outflows; many of the ELCs
may not survive as bound stellar systems, but rather dissipate rapidly into the
field population. The observed tendency of older ELCs to be more compact than
young ones is consistent with the preferential survival of the most
concentrated clusters at a given age. | 0706.3935v1 |
2007-06-29 | Reliable Final Computational Results from Faulty Quantum Computation | In this paper we extend both standard fault tolerance theory and Kitaev's
model for quantum computation, combining them so as to yield quantitative
results that reveal the interplay between the two. Our analysis establishes a
methodology that allows us to quantitatively determine design parameters for a
quantum computer, the values of which ensure that an overall computation of
interest yields a correct *final result* with some prescribed probability of
success, as opposed to merely ensuring that the desired *final quantum state*
is obtained. As a specific example of the practical application of our
approach, we explicitly calculate the number of levels of error correction
concatenation needed to achieve a correct final result for the overall
computation with some prescribed success probability. Since our methodology
allows one to determine parameters required in order to achieve the correct
final result for the overall quantum computation, as opposed to merely ensuring
that the desired final quantum state is produced, our method enables the
determination of complete quantum computational resource requirements
associated to the actual solution of practical problems. | 0707.0008v1 |
2007-08-24 | Quantum Sensor Miniaturization | The classical bound on image resolution defined by the Rayleigh limit can be
beaten by exploiting the properties of quantum mechanical entanglement. If
entangled photons are used as signal states, the best possible resolution is
instead given by the Heisenberg limit, an improvement proportional to the
number of entangled photons in the signal. In this paper we present a novel
application of entanglement by showing that the resolution obtained by an
imaging system utilizing separable photons can be achieved by an imaging system
making use of entangled photons, but with the advantage of a smaller aperture,
thus resulting in a smaller and lighter system. This can be especially valuable
in satellite imaging where weight and size play a vital role. | 0708.3403v1 |
2007-09-02 | A Universal Operator Theoretic Framework for Quantum Fault Tolerance | In this paper we introduce a universal operator theoretic framework for
quantum fault tolerance. This incorporates a top-down approach that implements
a system-level criterion based on specification of the full system dynamics,
applied at every level of error correction concatenation. This leads to more
accurate determinations of error thresholds than could previously be obtained.
This is demonstrated both formally and with an explicit numerical example. The
basis for our approach is the Quantum Computer Condition (QCC), an inequality
governing the evolution of a quantum computer. We show that all known coding
schemes are actually special cases of the QCC. We demonstrate this by
introducing a new, operator theoretic form of entanglement assisted quantum
error correction, which incorporates as special cases all known error
correcting protocols, and is itself a special case of the QCC. | 0709.0128v3 |
2007-10-25 | Ordering in red abalone nacre | Red abalone nacre is an intensely studied biomineral, and yet its formation
mechanism remains poorly understood. Here we report quantitative measurements
probing the degree of order of the aragonite tablets in nacre, and show that
order develops over a distance of about 50 microns. These observations indicate
that the orientational order of aragonite tablets in nacre is established
gradually and dynamically, and we show that a model of controlled assembly
based on suppression of the crystal growth rate along a specific direction,
when growth is confined in a layered structure, yields a tablet pattern
consistent with those revealed by detailed experimental measurements. This work
provides strong evidence that the organism s control of crystal orientation in
nacre occurs via regulation of crystal nucleation and growth as opposed to
direct templation or heteroepitaxial growth on organic molecules on the organic
matrix sheets. | 0710.4573v1 |
2007-11-01 | Interaction effects in mixed-valent Kondo insulators | We study theoretically the class of mixed-valent Kondo insulators, employing
a recently developed local moment approach to heavy Fermion systems using the
asymmetric periodic Anderson model (PAM). Novel features in spectra and
transport, observable experimentally but lying outside the scope of the
symmetric PAM or the Kondo lattice model, emerge naturally within the present
theory. We argue in particular that a shoulder-like feature in the optical
conductivity, that is distinct from the usual mid-infrared or direct gap peak
and has been observed experimentally in mixed-valent compounds such as
CeOs4Sb12 and YbAl3, is of intrinsic origin. Detailed comparison is made
between the resultant theory and transport/optical experiments on the
filled-skutterudite compound CeOs4Sb12, and good agreement is obtained. | 0711.0121v1 |
2008-01-31 | Counting growth types of automorphisms of free groups | Given an automorphism of a free group $F_n$, we consider the following
invariants: $e$ is the number of exponential strata (an upper bound for the
number of different exponential growth rates of conjugacy classes); $d$ is the
maximal degree of polynomial growth of conjugacy classes; $R$ is the rank of
the fixed subgroup. We determine precisely which triples $(e,d,R)$ may be
realized by an automorphism of $F_n$. In particular, the inequality $e\le
(3n-2)/4}$ (due to Levitt-Lustig) always holds. In an appendix, we show that
any conjugacy class grows like a polynomial times an exponential under
iteration of the automorphism. | 0801.4844v2 |
2008-04-29 | Combining geometry and combinatorics: A unified approach to sparse signal recovery | There are two main algorithmic approaches to sparse signal recovery:
geometric and combinatorial. The geometric approach starts with a geometric
constraint on the measurement matrix and then uses linear programming to decode
information about the signal from its measurements. The combinatorial approach
constructs the measurement matrix and a combinatorial decoding algorithm to
match. We present a unified approach to these two classes of sparse signal
recovery algorithms.
The unifying elements are the adjacency matrices of high-quality unbalanced
expanders. We generalize the notion of Restricted Isometry Property (RIP),
crucial to compressed sensing results for signal recovery, from the Euclidean
norm to the l_p norm for p about 1, and then show that unbalanced expanders are
essentially equivalent to RIP-p matrices.
From known deterministic constructions for such matrices, we obtain new
deterministic measurement matrix constructions and algorithms for signal
recovery which, compared to previous deterministic algorithms, are superior in
either the number of measurements or in noise tolerance. | 0804.4666v1 |
2008-08-08 | Heat conductivity from molecular chaos hypothesis in locally confined billiard systems | We study the transport properties of a large class of locally confined
Hamiltonian systems, in which neighboring particles interact through hard core
elastic collisions. When these collisions become rare and the systems large, we
derive a Boltzmann-like equation for the evolution of the probability
densities. We solve this equation in the linear regime and compute the heat
conductivity from a Green-Kubo formula. The validity of our approach is
demonstated by comparing our predictions to the results of numerical
simulations performed on a new class of high-dimensional defocusing chaotic
billiards. | 0808.1179v2 |
2008-09-23 | On the derivation of Fourier's law in stochastic energy exchange systems | We present a detailed derivation of Fourier's law in a class of stochastic
energy exchange systems that naturally characterize two-dimensional mechanical
systems of locally confined particles in interaction. The stochastic systems
consist of an array of energy variables which can be partially exchanged among
nearest neighbours at variable rates. We provide two independent derivations of
the thermal conductivity and prove this quantity is identical to the frequency
of energy exchanges. The first derivation relies on the diffusion of the
Helfand moment, which is determined solely by static averages. The second
approach relies on a gradient expansion of the probability measure around a
non-equilibrium stationary state. The linear part of the heat current is
determined by local thermal equilibrium distributions which solve a
Boltzmann-like equation. A numerical scheme is presented with computations of
the conductivity along our two methods. The results are in excellent agreement
with our theory. | 0809.3967v2 |
2008-10-19 | Coding Theorems for Repeat Multiple Accumulate Codes | In this paper the ensemble of codes formed by a serial concatenation of a
repetition code with multiple accumulators connected through random
interleavers is considered. Based on finite length weight enumerators for these
codes, asymptotic expressions for the minimum distance and an arbitrary number
of accumulators larger than one are derived using the uniform interleaver
approach. In accordance with earlier results in the literature, it is first
shown that the minimum distance of repeat-accumulate codes can grow, at best,
sublinearly with block length. Then, for repeat-accumulate-accumulate codes and
rates of 1/3 or less, it is proved that these codes exhibit asymptotically
linear distance growth with block length, where the gap to the
Gilbert-Varshamov bound can be made vanishingly small by increasing the number
of accumulators beyond two. In order to address larger rates, random puncturing
of a low-rate mother code is introduced. It is shown that in this case the
resulting ensemble of repeat-accumulate-accumulate codes asymptotically
achieves linear distance growth close to the Gilbert-Varshamov bound. This
holds even for very high rate codes. | 0810.3422v1 |
2008-12-09 | Statistical properties of time-reversible triangular maps of the square | Time reversal symmetric triangular maps of the unit square are introduced
with the property that the time evolution of one of their two variables is
determined by a piecewise expanding map of the unit interval. We study their
statistical properties and establish the conditions under which their
equilibrium measures have a product structure, i.e. factorises in a symmetric
form. When these conditions are not verified, the equilibrium measure does not
have a product form and therefore provides additional information on the
statistical properties of theses maps. This is the case of anti-symmetric cusp
maps, which have an intermittent fixed point and yet have uniform invariant
measures on the unit interval. We construct the invariant density of the
corresponding two-dimensional triangular map and prove that it exhibits a
singularity at the intermittent fixed point. | 0812.1648v1 |
2009-03-20 | Fractality of the non-equilibrium stationary states of open volume-preserving systems: I. Tagged particle diffusion | Deterministic diffusive systems such as the periodic Lorentz gas, multi-baker
map, as well as spatially periodic systems of interacting particles, have
non-equilibrium stationary states with fractal properties when put in contact
with particle reservoirs at their boundaries. We study the macroscopic limits
of these systems and establish a correspondence between the thermodynamics of
the macroscopic diffusion process and the fractality of the stationary states
that characterize the phase-space statistics. In particular the entropy
production rate is recovered from first principles using a formalism due to
Gaspard [J. Stat. Phys. 88, 1215 (1997)]. This article is the first of two; the
second article considers the influence of a uniform external field on such
systems. | 0903.3476v1 |
2009-03-20 | Fractality of the non-equilibrium stationary states of open volume-preserving systems: II. Galton boards | Galton boards are models of deterministic diffusion in a uniform external
field, akin to driven periodic Lorentz gases, here considered in the absence of
dissipation mechanism. Assuming a cylindrical geometry with axis along the
direction of the external field, the two-dimensional board becomes a model for
one-dimensional mass transport along the direction of the external field. This
is a purely diffusive process which admits fractal non-equilibrium stationary
states under flux boundary conditions. Analytical results are obtained for the
statistics of multi-baker maps modeling such a non-uniform diffusion process. A
correspondence is established between the local phase-space statistics and
their macroscopic counter-parts. The fractality of the invariant state is shown
to be responsible for the positiveness of the entropy production rate. | 0903.3849v1 |
2009-07-23 | On Possible Variation in the Cosmological Baryon Fraction | The fraction of matter that is in the form of baryons or dark matter could
have spatial fluctuations in the form of baryon-dark matter isocurvature
fluctuations. We use big bang nucleosynthesis calculations compared with
observed light element abundances as well as galaxy cluster gas fractions to
constrain cosmological variations in the baryon fraction. Light element
abundances constrain spatial variations to be less than 26-27%, while a sample
of "relaxed" galaxy clusters shows spatial variations in gas fractions less
than 8%. Larger spatial variations could cause differential screening of the
primary cosmic microwave background anisotropies, leading to asymmetries in the
fluctuations and ease some tension with the halo-star 7Li abundance.
Fluctuations within our allowed bounds can lead to "B-mode" CMB polarization
anisotropies at a non-negligible level. | 0907.3919v2 |
2009-08-28 | Chaos in cylindrical stadium billiards via a generic nonlinear mechanism | We describe conditions under which higher-dimensional billiard models in
bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium
to dimensions above two. An example is a three-dimensional stadium bounded by a
cylinder and several planes; the combination of these elements may give rise to
defocusing, allowing large chaotic regions in phase space. By studying families
of marginally-stable periodic orbits that populate the residual part of phase
space, we identify conditions under which a nonlinear instability mechanism
arises in their vicinity. For particular geometries, this mechanism rather
induces stable nonlinear oscillations, including in the form of
whispering-gallery modes. | 0908.4243v2 |
2009-09-23 | The Gilbert Arborescence Problem | We investigate the problem of designing a minimum cost flow network
interconnecting n sources and a single sink, each with known locations in a
normed space and with associated flow demands. The network may contain any
finite number of additional unprescribed nodes from the space; these are known
as the Steiner points. For concave increasing cost functions, a minimum cost
network of this sort has a tree topology, and hence can be called a Minimum
Gilbert Arborescence (MGA). We characterise the local topological structure of
Steiner points in MGAs, showing, in particular, that for a wide range of
metrics, and for some typical real-world cost-functions, the degree of each
Steiner point is 3. | 0909.4270v2 |
2010-08-12 | Magnetization dynamics in the inertial regime: nutation predicted at short time scales | The dynamical equation of the magnetization has been reconsidered with
enlarging the phase space of the ferromagnetic degrees of freedom to the
angular momentum. The generalized Landau-Lifshitz-Gilbert equation that
includes inertial terms, and the corresponding Fokker-Planck equation, are then
derived in the framework of mesoscopic non-equilibrium thermodynamics theory. A
typical relaxation time $\tau$ is introduced describing the relaxation of the
magnetization acceleration from the inertial regime towards the precession
regime defined by a constant Larmor frequency. For time scales larger than
$\tau$, the usual Gilbert equation is recovered. For time scales below $\tau$,
nutation and related inertial effects are predicted. The inertial regime offers
new opportunities for the implementation of ultrafast magnetization switching
in magnetic devices. | 1008.2177v1 |
2010-11-03 | Existence of vertical spin stiffness in Landau-Lifshitz-Gilbert equation in ferromagnetic semiconductors | We calculate the magnetization torque due to the spin polarization of the
itinerant electrons by deriving the kinetic spin Bloch equations based on the
$s$-$d$ model. We find that the first-order gradient of the magnetization
inhomogeneity gives rise to the current-induced torques, which are consistent
to the previous works. At the second-order gradient, we find an effective
magnetic field perpendicular to the spin stiffness filed. This field is
proportional to the nonadiabatic parameter $\beta$. We show that this vertical
spin stiffness term can significantly modify the domain-wall structure in
ferromagnetic semiconductors and hence should be included in the
Landau-Lifshitz-Gilbert equation in studying the magnetization dynamics. | 1011.0871v1 |
2011-01-05 | The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview | The Landau-Lifshitz-Gilbert (LLG) equation is a fascinating nonlinear
evolution equation both from mathematical and physical points of view. It is
related to the dynamics of several important physical systems such as
ferromagnets, vortex filaments, moving space curves, etc. and has intimate
connections with many of the well known integrable soliton equations, including
nonlinear Schr\"odinger and sine-Gordon equations. It can admit very many
dynamical structures including spin waves, elliptic function waves, solitons,
dromions, vortices, spatio-temporal patterns, chaos, etc. depending on the
physical and spin dimensions and the nature of interactions. An exciting recent
development is that the spin torque effect in nanoferromagnets is described by
a generalization of the LLG equation which forms a basic dynamical equation in
the field of spintronics. This article will briefly review these developments
as a tribute to Robin Bullough who was a great admirer of the LLG equation. | 1101.1005v1 |
2011-02-05 | Graph Theory | This is a replacement paper. There are 6 chapters. The first two chapters are
introductory. The third chapter is on extremal graph theory. The fourth chapter
is about algebra in graph theory. The fifth chapter is focused on algorithms.
The third section of the fifth chapter deals with computable time. The sixth
chapter has sections on probability and enumeration. | 1102.1087v11 |
2011-04-28 | The High-Redshift Neutral Hydrogen Signature of an Anisotropic Matter Power Spectrum | An anisotropic power spectrum will have a clear signature in the 21cm
radiation from high-redshift hydrogen. We calculate the expected power spectrum
of the intensity fluctuations in neutral hydrogen from before the epoch of
reionization, and predict the accuracy to which future experiments could
constrain a quadrupole anisotropy in the power spectrum. We find that the
Square Kilometer Array will have marginal detection abilities for this signal
at z~17 if the process of reionization has not yet started; reionization could
enhance the detectability substantially. Pushing to higher redshifts and higher
sensitivity will allow highly precise (percent level) measurements of
anisotropy. | 1104.5403v3 |
2011-06-30 | A generalisation of the Gilbert-Varshamov bound and its asymptotic evaluation | The Gilbert-Varshamov (GV) lower bound on the maximum cardinality of a q-ary
code of length n with minimum Hamming distance at least d can be obtained by
application of Turan's theorem to the graph with vertex set {0,1,..,q-1}^n in
which two vertices are joined if and only if their Hamming distance is at least
d. We generalize the GV bound by applying Turan's theorem to the graph with
vertex set C^n, where C is a q-ary code of length m and two vertices are joined
if and only if their Hamming distance at least d. We asymptotically evaluate
the resulting bound for n-> \infty and d \delta mn for fixed \delta > 0, and
derive conditions on the distance distribution of C that are necessary and
sufficient for the asymptotic generalized bound to beat the asymptotic GV
bound. By invoking the Delsarte inequalities, we conclude that no improvement
on the asymptotic GV bound is obtained. By using a sharpening of Turan's
theorem due to Caro and Wei, we improve on our bound. It is undecided if there
exists a code C for which the improved bound can beat the asymptotic GV bound. | 1106.6206v1 |
2011-07-17 | Probabilistic Methods on Erdos Problems | The paper reviews and tries to describe the reference set method, which is a
method of combinatorial optimization that gives upper bounds on parameters. | 1107.3279v17 |
2011-09-12 | Externally-driven transmission and collisions of domain walls in ferromagnetic wires | Analytical multi-domain solutions to the dynamical (Landau-Lifshitz-Gilbert)
equation of a one-dimensional ferromagnet including an external magnetic field
and spin-polarized electric current are found using the Hirota bilinearization
method. A standard approach to solve the Landau-Lifshitz equation (without the
Gilbert term) is modified in order to treat the dissipative dynamics. I
establish the relations between the spin interaction parameters (the constants
of exchange, anisotropy, dissipation, external-field intensity, and
electric-current intensity) and the domain-wall parameters (width and velocity)
and compare them to the results of the Walker approximation and micromagnetic
simulations. The domain-wall motion driven by a longitudinal external field is
analyzed with especial relevance to the field-induced collision of two domain
walls. I determine the result of such a collision (which is found to be the
elastic one) on the domain-wall parameters below and above the Walker breakdown
(in weak- and strong-field regimes). Single-domain-wall dynamics in the
presence of an external transverse field is studied with relevance to the
challenge of increasing the domain-wall velocity below the breakdown. | 1109.2465v1 |
2011-10-19 | Current-induced switching in transport through anisotropic magnetic molecules | Anisotropic single-molecule magnets may be thought of as molecular switches,
with possible applications to molecular spintronics. In this paper, we consider
current-induced switching in single-molecule junctions containing an
anisotropic magnetic molecule. We assume that the carriers interact with the
magnetic molecule through the exchange interaction and focus on the regime of
high currents in which the molecular spin dynamics is slow compared to the time
which the electrons spend on the molecule. In this limit, the molecular spin
obeys a non-equilibrium Langevin equation which takes the form of a generalized
Landau-Lifshitz-Gilbert equation and which we derive microscopically by means
of a non-equilibrium Born-Oppenheimer approximation. We exploit this Langevin
equation to identify the relevant switching mechanisms and to derive the
current-induced switching rates. As a byproduct, we also derive S-matrix
expressions for the various torques entering into the Landau-Lifshitz-Gilbert
equation which generalize previous expressions in the literature to
non-equilibrium situations. | 1110.4270v2 |
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